Byzantine-robust decentralized deterministic optimization methods have been developed in [1]}, [2]}, where at every iteration every regular agent uses all of its local data samples, instead of one or a batch. The work of [1]} proposes ByRDiE, in which every regular agent utilizes coordinate-wise trimmed mean to screen outliers in the received models, and then applies coordinate gradient descent to update its local model. The one-coordinate-at-a-time update of ByRDiE is inefficient for high-dimensional problems [2]}. To address this issue, the work of [2]} proposes BRIDGE, which allows every regular agent to update all the coordinates of its local model at every iteration. Although these two algorithms are originally developed for decentralized deterministic optimization, they can also be adapted to the decentralized stochastic setting according to our numerical experiments. However, to the best of our knowledge, most of the existing works do not explicitly consider the Byzantine-robust decentralized stochastic optimization problem; see for reference the recent survey paper [6]}.
